OK, so I'll try to address some of the errors in your analysis:
1. ANY kind of an ultra-simplified flat or fair tax would, by definition, be stimulatory. Administering either would require a far smaller bureaucracy. Every dollar the federal government collects is a dollar removed from the real economy; federal bureaucracy jobs are economy dampeners. An "IRS" shrunk to 1/10th it's current size would be highly, highly stimulatory.
2. "Selling goods & services" is partially correct - because doing so equates to jobs - but doing so DOMESTICALLY is simply an economy standing in a pail and tugging on the handle in a vain attempt to lift the pail. EXPORTS of goods and services would be a true economy stimulator. A national sales tax would not hinder exports.
3. Both a national sales tax and a flat-rate income tax have advantages and disadvantages - primarily in that both can be gamed and thus require a federal bureaucracy of some sort to administer. Many believe a sales tax would be less easily 'gamed' and thus could theoretically be administered with a smaller bureaucracy. However, either would be preferable to the current mess.
4. A flat tax is not more likely to generate a steady revenue stream since both fair & flat depend on economic activity.
5. The key unspoken problem with both fair & flat is the liklihood of "The Enemy" (those in Washington DC) to simply layer the new tax ON TOP OF the existing system rather than replace it. I consider this almost a certainty (though, initially, the scoundrels would probably at least reduce the current tax rates so as to appear to the masses to not have done the above). Given time I see both Fair & Flat as simply a way to INCREASE government revenue and thus support more government spending. Perhaps a Flat Income Tax has a slightly higher chance of being a complete replacement for the existing system ... but I'm not optimistic the scoundrels would not 'find a way'.